Constraint-Induced Crack Initiation and Crack Growth at Electrode Edges in Piezoelectric Ceramics

Piezoelectric ceramic actuators are nowadays used for numerous applications in adaptive structures and vibration control. Respective components have been accepted in the aircraft and automobile industry as well as in printing and textile machinery. Albeit exhibiting some ferroelastic toughening, the fracture toughness of ferroelectric actuator materials is rather small. They are susceptible to fracture under high electric fields or mechanical stresses. Therefore, the limited reliability of the component due to cracking constitutes a major impediment to large scale usage. A cost efficient geometry for actuators with large displacements is that of the cofired multilayer geometry. The common design consists of two interdigitated electrodes. This geometry carries the disadvantage of electrodes ending inside the ceramic. As a consequence, the ceramic material, which exhibits ferroelectric, ferroelastic as well as piezoelectric behavior, experiences a strain incompatibility between the electrically active and inactive material regions. A complex mechanical stress field originating at the electrode edge arises and can lead to crack initiation in this area, crack growth, and finally to the failure of the device. To obtain a better understanding of the underlying mechanisms crack nucleation and crack propagation have to be separated. In ferroelectric ceramics crack nucleation is governed by statistics of defects. Knowledge of the geometrical and electrical conditions resulting in critical stresses is therefore required. After crack initiation the crack propagation is the dominant mechanism which is characterized by an equilibrium of crack driving and crack resistance forces. Both are highly dependent on the geometry and the applied boundary conditions. The present work provides a study of crack nucleation as well as crack propagation in model geometries under various electrical and mechanical boundary conditions. Non-linear finite element modelling and fracture mechanical analysis are used to investigate the material response and the equilibrium conditions.

Keramische Vielschichtaktuatoren werden in zahlreichen Anwendungen eingesetzt, in denen es auf schnelle und genaue Positionierung bei verhältnismäßig großen Verstellwegen ankommt. Die kostengünstigste Herstellungsweise dieser Aktuatoren setzt eine kammartige Anordnung der Elektroden voraus. Die dadurch bedingten internen Elektrodenkanten führen zu einer nur teilweisen Elektrodenbedeckung, die ihrerseits zu einer Dehungungsinkompatibilität zwischen den aktiven und inaktiven Bereichen im Bauelement führt. Die daraus resultierenden Risse führen schließlich zum Versagen des gesamten Bauteils. In der vorliegenden Arbeit wird die Rißentstehung und das Rißwachstum an Modellexperimenten unter verschiedenen elektrischen und mechanischen Randbedingungen untersucht. Dabei wird die partielle Elektrodenbedeckung im Aktuator durch dünne Scheiben einer piezoelektrischen Keramik (PZT) mit unterschiedlichen Geometrien, Elektrodenbedeckungen und Probendicken modelliert. Nichtlineare finite Elemente Modellierung und bruchmechanische Analysen werden herangezogen, um das Materialverhalten und die vorliegenden Gleichgewichtsbedingungen zu untersuchen.